协变量缺失下部分线性模型的模型选择和模型平均  

Model Selection and Model Averaging for Partially Linear Models with Missing Covariates

作　　者：胡国治 程维虎[1] 曾婕[1,2] HU GUOZHI;CHENG WEIHU;ZENG JIE(College of Applied Science,Beijing University of Technology,Berijing 100124;College of Mathermatics and Statistics,Hefei Normal University,Hefei 230601)

机构地区：[1]北京工业大学应用数理学院,北京100124 [2]合肥师范学院数学与统计学院,合肥230601

出　　处：《应用数学学报》2020年第3期535-554,共20页Acta Mathematicae Applicatae Sinica

摘　　要：本文研究了协变量随机缺失下部分线性模型的模型选择和模型平均问题.首先利用逆概率加权方法得出了线性回归系数和非参数函数的估计,并在局部误设定框架下证明了线性回归系数估计量的渐近正态性.然后构造了兴趣参数的兴趣信息准则和频数模型平均估计量,并根据该模型平均估计量构造了一个覆盖真实参数的概率趋于预定水平的置信区间.模拟研究和实例分析分别说明了本方法的优越性和实用性.This paper concerns with model selection and model averaging for partially linear models with missing covariates.The inverse probability weighted method is employed to estimate the linear regression coefficients and the nonparametric function,and the estimators of the linear parameters are shown to be asymptotically normal under the local misspecification framework.Then we develop the focused information criterion and the frequentist model average estimator for the focus parameter,and construct a confidence interval having a coverage probability that tends toward the intended level based on the model average estimator.Simulation study and real data analysis are performed to respectively demonstrate the superiority and practicability of the proposed methods.

关 键 词：部分线性模型 模型选择 模型平均 协变量缺失 

分 类 号：O212.7[理学—概率论与数理统计]